Tian, Hao; Yang, Xianchu; Liu, Chenguang; Liu, Guilin A fast implementation of the linear bond-based peridynamic beam model. (English) Zbl 07800004 Adv. Appl. Math. Mech. 16, No. 2, 305-330 (2024). MSC: 65R20 65Y10 PDFBibTeX XMLCite \textit{H. Tian} et al., Adv. Appl. Math. Mech. 16, No. 2, 305--330 (2024; Zbl 07800004) Full Text: DOI
D’Elia, Marta; Littlewood, David J.; Trageser, Jeremy; Perego, Mauro; Bochev, Pavel B. An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions. (English) Zbl 07814300 Mengesha, Tadele (ed.) et al., A\(^3\) N\(^2\) M: approximation, applications, and analysis of nonlocal, nonlinear models. Proceedings of the 50th John H. Barrett memorial lectures, Knoxville, TN, USA, virtual, May 2021. Cham: Springer. IMA Vol. Math. Appl. 165, 151-174 (2023). MSC: 74S05 35Q74 35R11 65M60 74A45 PDFBibTeX XMLCite \textit{M. D'Elia} et al., IMA Vol. Math. Appl. 165, 151--174 (2023; Zbl 07814300) Full Text: DOI arXiv
Pang, Gang; Ji, Songsong; Chao, Leiyu A second-order absorbing boundary condition for two-dimensional peridynamics. (English) Zbl 07787604 ESAIM, Math. Model. Numer. Anal. 57, No. 5, 3029-3059 (2023). MSC: 65L20 65L10 65L12 PDFBibTeX XMLCite \textit{G. Pang} et al., ESAIM, Math. Model. Numer. Anal. 57, No. 5, 3029--3059 (2023; Zbl 07787604) Full Text: DOI
Klar, Manuel; Capodaglio, Giacomo; D’Elia, Marta; Glusa, Christian; Gunzburger, Max; Vollmann, Christian A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type. (English) Zbl 07783952 Comput. Math. Appl. 151, 434-448 (2023). MSC: 45K05 65N30 35R11 65M60 45A05 PDFBibTeX XMLCite \textit{M. Klar} et al., Comput. Math. Appl. 151, 434--448 (2023; Zbl 07783952) Full Text: DOI arXiv
Scabbia, Francesco; Gasparrini, Claudia; Zaccariotto, Mirco; Galvanetto, Ugo; Larios, Adam; Bobaru, Florin Moving interfaces in peridynamic diffusion models and the influence of discontinuous initial conditions: numerical stability and convergence. (English) Zbl 07783948 Comput. Math. Appl. 151, 384-396 (2023). MSC: 74A45 74B99 80A20 74A70 65M12 PDFBibTeX XMLCite \textit{F. Scabbia} et al., Comput. Math. Appl. 151, 384--396 (2023; Zbl 07783948) Full Text: DOI
Hermann, Alexander; Shojaei, Arman; Seleson, Pablo; Cyron, Christian J.; Silling, Stewart A. Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media. (English) Zbl 07772278 Int. J. Numer. Methods Eng. 124, No. 16, 3524-3553 (2023). MSC: 74Sxx 65Dxx 65Mxx PDFBibTeX XMLCite \textit{A. Hermann} et al., Int. J. Numer. Methods Eng. 124, No. 16, 3524--3553 (2023; Zbl 07772278) Full Text: DOI OA License
Acosta, Gabriel; Bersetche, Francisco M.; Rossi, Julio D. A domain decomposition scheme for couplings between local and nonlocal equations. (English) Zbl 07766465 Comput. Methods Appl. Math. 23, No. 4, 817-830 (2023). MSC: 65-XX 35R11 45K05 65N30 47G20 PDFBibTeX XMLCite \textit{G. Acosta} et al., Comput. Methods Appl. Math. 23, No. 4, 817--830 (2023; Zbl 07766465) Full Text: DOI arXiv
Mengesha, Tadele; Salgado, Abner J.; Siktar, Joshua M. On the optimal control of a linear peridynamics model. (English) Zbl 1523.45002 Appl. Math. Optim. 88, No. 3, Paper No. 70, 43 p. (2023). Reviewer: Kai Diethelm (Schweinfurt) MSC: 45F15 49M41 49M25 49J21 65R20 74P10 74A45 PDFBibTeX XMLCite \textit{T. Mengesha} et al., Appl. Math. Optim. 88, No. 3, Paper No. 70, 43 p. (2023; Zbl 1523.45002) Full Text: DOI arXiv
Zhang, Qi; Nguyen-Thanh, Nhon; Li, Weidong; Zhang, A-Man; Li, Shaofan; Zhou, Kun A coupling approach of the isogeometric-meshfree method and peridynamics for static and dynamic crack propagation. (English) Zbl 07737561 Comput. Methods Appl. Mech. Eng. 410, Article ID 115904, 30 p. (2023). MSC: 74-XX 65-XX PDFBibTeX XMLCite \textit{Q. Zhang} et al., Comput. Methods Appl. Mech. Eng. 410, Article ID 115904, 30 p. (2023; Zbl 07737561) Full Text: DOI
Lu, Jiashu; Zhang, Qingyu; Zhao, Lijing; Nie, Yufeng An efficient Jacobi spectral collocation method with nonlocal quadrature rules for multi-dimensional volume-constrained nonlocal models. (English) Zbl 07714972 Int. J. Comput. Methods 20, No. 5, Article ID 2350004, 16 p. (2023). MSC: 65-XX 81-XX PDFBibTeX XMLCite \textit{J. Lu} et al., Int. J. Comput. Methods 20, No. 5, Article ID 2350004, 16 p. (2023; Zbl 07714972) Full Text: DOI
Glusa, Christian; D’Elia, Marta; Capodaglio, Giacomo; Gunzburger, Max; Bochev, Pavel B. An asymptotically compatible coupling formulation for nonlocal interface problems with jumps. (English) Zbl 07704386 SIAM J. Sci. Comput. 45, No. 3, A1359-A1384 (2023). MSC: 65-XX 35R11 65R20 PDFBibTeX XMLCite \textit{C. Glusa} et al., SIAM J. Sci. Comput. 45, No. 3, A1359--A1384 (2023; Zbl 07704386) Full Text: DOI arXiv
Rakici, Semsi; Kim, Jinseok A discrete surface correction method for bond-based peridynamics. (English) Zbl 1521.74400 Eng. Anal. Bound. Elem. 151, 115-135 (2023). MSC: 74S60 65M75 PDFBibTeX XMLCite \textit{S. Rakici} and \textit{J. Kim}, Eng. Anal. Bound. Elem. 151, 115--135 (2023; Zbl 1521.74400) Full Text: DOI
Li, Zhiyuan; Huang, Dan; Rabczuk, Timon Peridynamic operator method. (English) Zbl 07692950 Comput. Methods Appl. Mech. Eng. 411, Article ID 116047, 30 p. (2023). MSC: 65-XX 81-XX PDFBibTeX XMLCite \textit{Z. Li} et al., Comput. Methods Appl. Mech. Eng. 411, Article ID 116047, 30 p. (2023; Zbl 07692950) Full Text: DOI
Wang, Longfei; Zhou, Xiaoping Field-enriched finite element method for simulating of three-dimensional crack propagation. (English) Zbl 1519.74072 Comput. Mech. 71, No. 6, 1119-1138 (2023). MSC: 74S05 74R10 74G70 65N12 65N15 PDFBibTeX XMLCite \textit{L. Wang} and \textit{X. Zhou}, Comput. Mech. 71, No. 6, 1119--1138 (2023; Zbl 1519.74072) Full Text: DOI
Sun, Linlin; Fu, Zhuojia; Chen, Zhikang A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis. (English) Zbl 07689961 Appl. Math. Comput. 439, Article ID 127600, 17 p. (2023). MSC: 65Nxx 74Sxx 74Jxx PDFBibTeX XMLCite \textit{L. Sun} et al., Appl. Math. Comput. 439, Article ID 127600, 17 p. (2023; Zbl 07689961) Full Text: DOI
Zhou, Guanglei; Liu, Jiangwei; Xu, Tao; Konietzky, Heinz; Zang, Chuanwei; Zhang, Guangchao; Chen, Miao A 2D/3D implicit gradient-enhanced nonlocal meso-scale damage model for deformation and fracturing of brittle materials. (English) Zbl 1521.74280 Eng. Anal. Bound. Elem. 150, 298-308 (2023). MSC: 74S05 74R05 65M60 PDFBibTeX XMLCite \textit{G. Zhou} et al., Eng. Anal. Bound. Elem. 150, 298--308 (2023; Zbl 1521.74280) Full Text: DOI
Qin, Mingqi; Yang, Diansen; Jia, Yun A meshless method coupling peridynamics with corrective smoothed particle method for predicting material failure. (English) Zbl 1521.74016 Eng. Anal. Bound. Elem. 147, 125-137 (2023). MSC: 74A70 74S05 65M60 PDFBibTeX XMLCite \textit{M. Qin} et al., Eng. Anal. Bound. Elem. 147, 125--137 (2023; Zbl 1521.74016) Full Text: DOI
Zhang, Ting; Zhou, Xiao-Ping Ordinary state-based peridynamic plastic model with Drucker-Prager criterion considering geometric nonlinearity. (English) Zbl 1510.74014 Appl. Math. Modelling 118, 212-235 (2023). MSC: 74C99 65M60 PDFBibTeX XMLCite \textit{T. Zhang} and \textit{X.-P. Zhou}, Appl. Math. Modelling 118, 212--235 (2023; Zbl 1510.74014) Full Text: DOI
Zhu, Jinggao; Ren, Xiaodan A dissipation informed peridynamic model for dynamic brittle fracture. (English) Zbl 1512.74091 Commun. Nonlinear Sci. Numer. Simul. 121, Article ID 107236, 25 p. (2023). MSC: 74R10 74A70 74S99 65T60 PDFBibTeX XMLCite \textit{J. Zhu} and \textit{X. Ren}, Commun. Nonlinear Sci. Numer. Simul. 121, Article ID 107236, 25 p. (2023; Zbl 1512.74091) Full Text: DOI
Sheikhbahaei, Pouria; Mossaiby, Farshid; Shojaei, Arman An efficient peridynamic framework based on the arc-length method for fracture modeling of brittle and quasi-brittle problems with snapping instabilities. (English) Zbl 07674318 Comput. Math. Appl. 136, 165-190 (2023). MSC: 74R05 65N35 74R10 PDFBibTeX XMLCite \textit{P. Sheikhbahaei} et al., Comput. Math. Appl. 136, 165--190 (2023; Zbl 07674318) Full Text: DOI
Khanwale, Makrand A.; Saurabh, Kumar; Ishii, Masado; Sundar, Hari; Rossmanith, James A.; Ganapathysubramanian, Baskar A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes. (English) Zbl 07649292 J. Comput. Phys. 475, Article ID 111874, 35 p. (2023). MSC: 65Mxx 76Mxx 76Dxx PDFBibTeX XMLCite \textit{M. A. Khanwale} et al., J. Comput. Phys. 475, Article ID 111874, 35 p. (2023; Zbl 07649292) Full Text: DOI arXiv
Yao, Wu-Wen; Zhou, Xiao-Ping Meshless numerical solution for nonlocal integral differentiation equation with application in peridynamics. (English) Zbl 07789065 Eng. Anal. Bound. Elem. 144, 569-582 (2022). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{W.-W. Yao} and \textit{X.-P. Zhou}, Eng. Anal. Bound. Elem. 144, 569--582 (2022; Zbl 07789065) Full Text: DOI
Lopez, Luciano; Pellegrino, Sabrina Francesca A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models. (English) Zbl 1527.65135 Int. J. Numer. Methods Eng. 123, No. 20, 4859-4876 (2022). MSC: 65N35 41A50 65T50 65M06 65M12 35R09 74B20 74R10 PDFBibTeX XMLCite \textit{L. Lopez} and \textit{S. F. Pellegrino}, Int. J. Numer. Methods Eng. 123, No. 20, 4859--4876 (2022; Zbl 1527.65135) Full Text: DOI
Diehl, Patrick; Lipton, Robert Quasistatic fracture using nonlinear-nonlocal elastostatics with explicit tangent stiffness matrix. (English) Zbl 07768023 Int. J. Numer. Methods Eng. 123, No. 18, 4183-4208 (2022). MSC: 74Rxx 65Fxx 35Qxx PDFBibTeX XMLCite \textit{P. Diehl} and \textit{R. Lipton}, Int. J. Numer. Methods Eng. 123, No. 18, 4183--4208 (2022; Zbl 07768023) Full Text: DOI
Mohajerani, Soheil; Wang, Gang “Touch-aware” contact model for peridynamics modeling of granular systems. (English) Zbl 07768008 Int. J. Numer. Methods Eng. 123, No. 17, 3850-3878 (2022). MSC: 65Nxx 74Sxx 35Qxx PDFBibTeX XMLCite \textit{S. Mohajerani} and \textit{G. Wang}, Int. J. Numer. Methods Eng. 123, No. 17, 3850--3878 (2022; Zbl 07768008) Full Text: DOI
Armandei, Mojtaba; Burgos, Diego F. S.; Savioli, Rafael The fractal version of the bond-based peridynamics method. (English) Zbl 07767248 Int. J. Numer. Methods Eng. 123, No. 3, 820-843 (2022). MSC: 74Axx 74Sxx 65-XX PDFBibTeX XMLCite \textit{M. Armandei} et al., Int. J. Numer. Methods Eng. 123, No. 3, 820--843 (2022; Zbl 07767248) Full Text: DOI
Bi, Mingchao; Ju, Lili; Tian, Hao A dual-horizon nonlocal diffusion model and its finite element discretization. (English) Zbl 1524.65960 Numer. Math., Theory Methods Appl. 15, No. 4, 990-1008 (2022). MSC: 65R20 65N35 74S05 PDFBibTeX XMLCite \textit{M. Bi} et al., Numer. Math., Theory Methods Appl. 15, No. 4, 990--1008 (2022; Zbl 1524.65960) Full Text: DOI
Kendibilir, A.; Kefal, A.; Sohouli, A.; Yildiz, M.; Koc, B.; Suleman, A. Peridynamics topology optimization of three-dimensional structures with surface cracks for additive manufacturing. (English) Zbl 1507.74309 Comput. Methods Appl. Mech. Eng. 401, Part B, Article ID 115665, 39 p. (2022). MSC: 74P15 49M41 65K10 74A70 PDFBibTeX XMLCite \textit{A. Kendibilir} et al., Comput. Methods Appl. Mech. Eng. 401, Part B, Article ID 115665, 39 p. (2022; Zbl 1507.74309) Full Text: DOI
Pang, Gang; Ji, Songsong; Antoine, Xavier Accurate absorbing boundary conditions for two-dimensional peridynamics. (English) Zbl 07561055 J. Comput. Phys. 466, Article ID 111351, 23 p. (2022). MSC: 65Mxx 35Rxx 65Nxx PDFBibTeX XMLCite \textit{G. Pang} et al., J. Comput. Phys. 466, Article ID 111351, 23 p. (2022; Zbl 07561055) Full Text: DOI
Fan, Yiming; Tian, Xiaochuan; Yang, Xiu; Li, Xingjie; Webster, Clayton; Yu, Yue An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. (English) Zbl 07561048 J. Comput. Phys. 465, Article ID 111376, 28 p. (2022). MSC: 65Nxx 65Cxx 60Hxx PDFBibTeX XMLCite \textit{Y. Fan} et al., J. Comput. Phys. 465, Article ID 111376, 28 p. (2022; Zbl 07561048) Full Text: DOI arXiv
Lopez, Luciano; Pellegrino, Sabrina Francesca A space-time discretization of a nonlinear peridynamic model on a 2D lamina. (English) Zbl 1524.65668 Comput. Math. Appl. 116, 161-175 (2022). MSC: 65M70 65M06 74R10 35R11 35L65 35R09 65N35 65T50 65M12 35Q74 PDFBibTeX XMLCite \textit{L. Lopez} and \textit{S. F. Pellegrino}, Comput. Math. Appl. 116, 161--175 (2022; Zbl 1524.65668) Full Text: DOI arXiv
Du, Yu; Zhang, Jiwei Numerical solution of a one-dimensional nonlocal Helmholtz equation by perfectly matched layers. (English) Zbl 1499.49083 Numer. Math., Theory Methods Appl. 15, No. 2, 387-414 (2022). MSC: 49M25 65N22 65N06 65R20 82C21 46N40 45A05 PDFBibTeX XMLCite \textit{Y. Du} and \textit{J. Zhang}, Numer. Math., Theory Methods Appl. 15, No. 2, 387--414 (2022; Zbl 1499.49083) Full Text: DOI arXiv
Fernando, Milinda; Sundar, Hari Scalable local timestepping on octree grids. (English) Zbl 07511033 SIAM J. Sci. Comput. 44, No. 2, C156-C183 (2022). MSC: 68U01 68W10 68U05 65M06 PDFBibTeX XMLCite \textit{M. Fernando} and \textit{H. Sundar}, SIAM J. Sci. Comput. 44, No. 2, C156--C183 (2022; Zbl 07511033) Full Text: DOI arXiv
Bekar, Ali Can; Madenci, Erdogan; Haghighat, Ehsan On the solution of hyperbolic equations using the peridynamic differential operator. (English) Zbl 1507.74450 Comput. Methods Appl. Mech. Eng. 391, Article ID 114574, 23 p. (2022). MSC: 74S05 65M60 74A70 PDFBibTeX XMLCite \textit{A. C. Bekar} et al., Comput. Methods Appl. Mech. Eng. 391, Article ID 114574, 23 p. (2022; Zbl 1507.74450) Full Text: DOI
Shojaei, Arman; Hermann, Alexander; Cyron, Christian J.; Seleson, Pablo; Silling, Stewart A. A hybrid meshfree discretization to improve the numerical performance of peridynamic models. (English) Zbl 1507.74058 Comput. Methods Appl. Mech. Eng. 391, Article ID 114544, 33 p. (2022). MSC: 74A70 65N35 PDFBibTeX XMLCite \textit{A. Shojaei} et al., Comput. Methods Appl. Mech. Eng. 391, Article ID 114544, 33 p. (2022; Zbl 1507.74058) Full Text: DOI
Jo, Gwanghyun; Ha, Youn Doh Effective multigrid algorithms for algebraic system arising from static peridynamic systems. (English) Zbl 1481.65258 Numer. Algorithms 89, No. 2, 885-904 (2022). MSC: 65N55 65H10 65F08 65F10 65F35 PDFBibTeX XMLCite \textit{G. Jo} and \textit{Y. D. Ha}, Numer. Algorithms 89, No. 2, 885--904 (2022; Zbl 1481.65258) Full Text: DOI
Bekar, Ali C.; Madenci, Erdogan Peridynamics enabled learning partial differential equations. (English) Zbl 07508517 J. Comput. Phys. 434, Article ID 110193, 35 p. (2021). MSC: 35Qxx 65Fxx 74Axx PDFBibTeX XMLCite \textit{A. C. Bekar} and \textit{E. Madenci}, J. Comput. Phys. 434, Article ID 110193, 35 p. (2021; Zbl 07508517) Full Text: DOI
Xu, Xiao; D’Elia, Marta; Foster, John T. A machine-learning framework for peridynamic material models with physical constraints. (English) Zbl 1507.74060 Comput. Methods Appl. Mech. Eng. 386, Article ID 114062, 16 p. (2021). MSC: 74A70 74S05 65M60 PDFBibTeX XMLCite \textit{X. Xu} et al., Comput. Methods Appl. Mech. Eng. 386, Article ID 114062, 16 p. (2021; Zbl 1507.74060) Full Text: DOI arXiv
Meng, Changyu; Wei, Haoyang; Chen, Hailong; Liu, Yongming Modeling plasticity of cubic crystals using a nonlocal lattice particle method. (English) Zbl 1502.74019 Comput. Methods Appl. Mech. Eng. 385, Article ID 114069, 21 p. (2021). MSC: 74C05 65N75 74E15 PDFBibTeX XMLCite \textit{C. Meng} et al., Comput. Methods Appl. Mech. Eng. 385, Article ID 114069, 21 p. (2021; Zbl 1502.74019) Full Text: DOI
Haghighat, Ehsan; Bekar, Ali Can; Madenci, Erdogan; Juanes, Ruben A nonlocal physics-informed deep learning framework using the peridynamic differential operator. (English) Zbl 1502.65172 Comput. Methods Appl. Mech. Eng. 385, Article ID 114012, 18 p. (2021). MSC: 65M99 68T07 74A70 PDFBibTeX XMLCite \textit{E. Haghighat} et al., Comput. Methods Appl. Mech. Eng. 385, Article ID 114012, 18 p. (2021; Zbl 1502.65172) Full Text: DOI arXiv
Mei, Tie; Zhao, Jiangming; Liu, Zian; Peng, Xuhao; Chen, Ziguang; Bobaru, Florin The role of boundary conditions on convergence properties of peridynamic model for transient heat transfer. (English) Zbl 1464.80005 J. Sci. Comput. 87, No. 2, Paper No. 50, 22 p. (2021). MSC: 80A19 35R09 80M20 80M10 65D32 65M12 74A45 35Q79 PDFBibTeX XMLCite \textit{T. Mei} et al., J. Sci. Comput. 87, No. 2, Paper No. 50, 22 p. (2021; Zbl 1464.80005) Full Text: DOI
Jafarzadeh, Siavash; Wang, Longzhen; Larios, Adam; Bobaru, Florin A fast convolution-based method for peridynamic transient diffusion in arbitrary domains. (English) Zbl 1506.74477 Comput. Methods Appl. Mech. Eng. 375, Article ID 113633, 26 p. (2021). MSC: 74S22 65M70 65Y10 74A70 PDFBibTeX XMLCite \textit{S. Jafarzadeh} et al., Comput. Methods Appl. Mech. Eng. 375, Article ID 113633, 26 p. (2021; Zbl 1506.74477) Full Text: DOI
Yang, Dong; He, Xiaoqiao; Zhu, Jiaqi; Bie, Zhiwu A novel damage model in the peridynamics-based cohesive zone method (PD-CZM) for mixed mode fracture with its implicit implementation. (English) Zbl 1506.74039 Comput. Methods Appl. Mech. Eng. 377, Article ID 113721, 32 p. (2021). MSC: 74A70 74S10 65N08 74R10 PDFBibTeX XMLCite \textit{D. Yang} et al., Comput. Methods Appl. Mech. Eng. 377, Article ID 113721, 32 p. (2021; Zbl 1506.74039) Full Text: DOI
Yu, Yue; You, Huaiqian; Trask, Nathaniel An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture. (English) Zbl 1506.74506 Comput. Methods Appl. Mech. Eng. 377, Article ID 113691, 36 p. (2021). MSC: 74S99 65M70 74A70 PDFBibTeX XMLCite \textit{Y. Yu} et al., Comput. Methods Appl. Mech. Eng. 377, Article ID 113691, 36 p. (2021; Zbl 1506.74506) Full Text: DOI arXiv
Bode, T.; Weißenfels, C.; Wriggers, P. A consistent peridynamic formulation for arbitrary particle distributions. (English) Zbl 1506.74033 Comput. Methods Appl. Mech. Eng. 374, Article ID 113605, 18 p. (2021). MSC: 74A70 74S05 74S22 65M75 PDFBibTeX XMLCite \textit{T. Bode} et al., Comput. Methods Appl. Mech. Eng. 374, Article ID 113605, 18 p. (2021; Zbl 1506.74033) Full Text: DOI
Russillo, Andrea Francesco; Failla, Giuseppe; Alotta, Gioacchino; Marotti de Sciarra, Francesco; Barretta, Raffaele On the dynamics of nano-frames. (English) Zbl 07314432 Int. J. Eng. Sci. 160, Article ID 103433, 23 p. (2021). MSC: 74-XX 65-XX PDFBibTeX XMLCite \textit{A. F. Russillo} et al., Int. J. Eng. Sci. 160, Article ID 103433, 23 p. (2021; Zbl 07314432) Full Text: DOI arXiv
D’Elia, Marta; Du, Qiang; Glusa, Christian; Gunzburger, Max; Tian, Xiaochuan; Zhou, Zhi Numerical methods for nonlocal and fractional models. (English) Zbl 07674560 Acta Numerica 29, 1-124 (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{M. D'Elia} et al., Acta Numerica 29, 1--124 (2020; Zbl 07674560) Full Text: DOI arXiv
Du, Ning; Guo, Xu; Wang, Hong A fast state-based peridynamic numerical model. (English) Zbl 1473.65037 Commun. Comput. Phys. 27, No. 1, 274-291 (2020). MSC: 65F10 65M70 65T50 74B15 PDFBibTeX XMLCite \textit{N. Du} et al., Commun. Comput. Phys. 27, No. 1, 274--291 (2020; Zbl 1473.65037) Full Text: DOI
Yan, Jiale; Li, Shaofan; Kan, Xingyu; Zhang, A-Man; Lai, Xin Higher-order nonlocal theory of updated Lagrangian particle hydrodynamics (ULPH) and simulations of multiphase flows. (English) Zbl 1506.76137 Comput. Methods Appl. Mech. Eng. 368, Article ID 113176, 28 p. (2020). MSC: 76M28 65M75 76Txx PDFBibTeX XMLCite \textit{J. Yan} et al., Comput. Methods Appl. Mech. Eng. 368, Article ID 113176, 28 p. (2020; Zbl 1506.76137) Full Text: DOI
Hashim, Nur A.; Coombs, W. M.; Augarde, C. E.; Hattori, G. An implicit non-ordinary state-based peridynamics with stabilised correspondence material model for finite deformation analysis. (English) Zbl 1506.74034 Comput. Methods Appl. Mech. Eng. 371, Article ID 113304, 32 p. (2020). MSC: 74A70 74S05 65N30 PDFBibTeX XMLCite \textit{N. A. Hashim} et al., Comput. Methods Appl. Mech. Eng. 371, Article ID 113304, 32 p. (2020; Zbl 1506.74034) Full Text: DOI Link
Prudhomme, Serge; Diehl, Patrick On the treatment of boundary conditions for bond-based peridynamic models. (English) Zbl 1506.74433 Comput. Methods Appl. Mech. Eng. 372, Article ID 113391, 23 p. (2020). MSC: 74S05 65N35 74A70 PDFBibTeX XMLCite \textit{S. Prudhomme} and \textit{P. Diehl}, Comput. Methods Appl. Mech. Eng. 372, Article ID 113391, 23 p. (2020; Zbl 1506.74433) Full Text: DOI arXiv
Zhang, Heng; Qiao, Pizhong Virtual crack closure technique in peridynamic theory. (English) Zbl 1506.74375 Comput. Methods Appl. Mech. Eng. 372, Article ID 113318, 18 p. (2020). MSC: 74R10 74S05 65M60 74A70 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{P. Qiao}, Comput. Methods Appl. Mech. Eng. 372, Article ID 113318, 18 p. (2020; Zbl 1506.74375) Full Text: DOI
Leng, Yu; Tian, Xiaochuan; Trask, Nathaniel A.; Foster, John T. Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation. (English) Zbl 1506.74478 Comput. Methods Appl. Mech. Eng. 370, Article ID 113264, 25 p. (2020). MSC: 74S22 65N35 65N12 74A70 PDFBibTeX XMLCite \textit{Y. Leng} et al., Comput. Methods Appl. Mech. Eng. 370, Article ID 113264, 25 p. (2020; Zbl 1506.74478) Full Text: DOI arXiv
Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon A higher order nonlocal operator method for solving partial differential equations. (English) Zbl 1442.65440 Comput. Methods Appl. Mech. Eng. 367, Article ID 113132, 26 p. (2020). MSC: 65N99 PDFBibTeX XMLCite \textit{H. Ren} et al., Comput. Methods Appl. Mech. Eng. 367, Article ID 113132, 26 p. (2020; Zbl 1442.65440) Full Text: DOI
Ni, Tao; Pesavento, Francesco; Zaccariotto, Mirco; Galvanetto, Ugo; Zhu, Qi-Zhi; Schrefler, Bernhard A. Hybrid FEM and peridynamic simulation of hydraulic fracture propagation in saturated porous media. (English) Zbl 1442.74212 Comput. Methods Appl. Mech. Eng. 366, Article ID 113101, 32 p. (2020). MSC: 74R10 74S05 65M60 74A70 74F10 76S05 PDFBibTeX XMLCite \textit{T. Ni} et al., Comput. Methods Appl. Mech. Eng. 366, Article ID 113101, 32 p. (2020; Zbl 1442.74212) Full Text: DOI
Liu, Shuo; Fang, Guodong; Liang, Jun; Fu, Maoqing; Wang, Bing A new type of peridynamics: element-based peridynamics. (English) Zbl 1442.74032 Comput. Methods Appl. Mech. Eng. 366, Article ID 113098, 25 p. (2020). MSC: 74A70 74S05 65N30 PDFBibTeX XMLCite \textit{S. Liu} et al., Comput. Methods Appl. Mech. Eng. 366, Article ID 113098, 25 p. (2020; Zbl 1442.74032) Full Text: DOI
You, Huaiqian; Yu, Yue; Kamensky, David An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions. (English) Zbl 1442.74244 Comput. Methods Appl. Mech. Eng. 366, Article ID 113038, 36 p. (2020). MSC: 74S05 45K05 35R09 65N30 74A15 PDFBibTeX XMLCite \textit{H. You} et al., Comput. Methods Appl. Mech. Eng. 366, Article ID 113038, 36 p. (2020; Zbl 1442.74244) Full Text: DOI arXiv
Bode, T.; Weißenfels, C.; Wriggers, P. Peridynamic Petrov-Galerkin method: a generalization of the peridynamic theory of correspondence materials. (English) Zbl 1441.74016 Comput. Methods Appl. Mech. Eng. 358, Article ID 112636, 21 p. (2020). MSC: 74A45 74S05 65N30 PDFBibTeX XMLCite \textit{T. Bode} et al., Comput. Methods Appl. Mech. Eng. 358, Article ID 112636, 21 p. (2020; Zbl 1441.74016) Full Text: DOI
Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon A nonlocal operator method for solving partial differential equations. (English) Zbl 1441.35250 Comput. Methods Appl. Mech. Eng. 358, Article ID 112621, 27 p. (2020). MSC: 35R09 35A25 58E30 65M99 PDFBibTeX XMLCite \textit{H. Ren} et al., Comput. Methods Appl. Mech. Eng. 358, Article ID 112621, 27 p. (2020; Zbl 1441.35250) Full Text: DOI arXiv
Coclite, G. M.; Fanizzi, A.; Lopez, L.; Maddalena, F.; Pellegrino, S. F. Numerical methods for the nonlocal wave equation of the peridynamics. (English) Zbl 1436.65195 Appl. Numer. Math. 155, 119-139 (2020). MSC: 65N35 65D30 65L06 35R09 45K05 74B10 35Q74 PDFBibTeX XMLCite \textit{G. M. Coclite} et al., Appl. Numer. Math. 155, 119--139 (2020; Zbl 1436.65195) Full Text: DOI arXiv
Shen, Feng; Yu, Yangtian; Zhang, Qing; Gu, Xin Hybrid model of peridynamics and finite element method for static elastic deformation and brittle fracture analysis. (English) Zbl 1464.74203 Eng. Anal. Bound. Elem. 113, 17-25 (2020). MSC: 74S05 74R10 65M60 PDFBibTeX XMLCite \textit{F. Shen} et al., Eng. Anal. Bound. Elem. 113, 17--25 (2020; Zbl 1464.74203) Full Text: DOI
Tian, Xiaochuan; Du, Qiang Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models. (English) Zbl 1485.65058 SIAM Rev. 62, No. 1, 199-227 (2020). MSC: 65J10 49M25 65N30 65R20 82C21 46N40 45A05 PDFBibTeX XMLCite \textit{X. Tian} and \textit{Q. Du}, SIAM Rev. 62, No. 1, 199--227 (2020; Zbl 1485.65058) Full Text: DOI
Tian, Hao; Zhang, Jing; Ju, Lili A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions. (English) Zbl 1433.65321 Appl. Math. Comput. 370, Article ID 124930, 15 p. (2020). MSC: 65N35 35K57 PDFBibTeX XMLCite \textit{H. Tian} et al., Appl. Math. Comput. 370, Article ID 124930, 15 p. (2020; Zbl 1433.65321) Full Text: DOI
Yan, Jiale; Li, Shaofan; Zhang, A-Man; Kan, Xingyu; Sun, Peng-Nan Updated Lagrangian particle hydrodynamics (ULPH) modeling and simulation of multiphase flows. (English) Zbl 1452.76186 J. Comput. Phys. 393, 406-437 (2019). MSC: 76M28 65M75 76N06 76D45 76T10 PDFBibTeX XMLCite \textit{J. Yan} et al., J. Comput. Phys. 393, 406--437 (2019; Zbl 1452.76186) Full Text: DOI
Gu, Xin; Zhang, Qing; Madenci, Erdogan; Xia, Xiaozhou Possible causes of numerical oscillations in non-ordinary state-based peridynamics and a bond-associated higher-order stabilized model. (English) Zbl 1442.74031 Comput. Methods Appl. Mech. Eng. 357, Article ID 112592, 36 p. (2019). MSC: 74A70 65M75 PDFBibTeX XMLCite \textit{X. Gu} et al., Comput. Methods Appl. Mech. Eng. 357, Article ID 112592, 36 p. (2019; Zbl 1442.74031) Full Text: DOI
Jha, Prashant K.; Lipton, Robert Numerical convergence of finite difference approximations for state based peridynamic fracture models. (English) Zbl 1441.74018 Comput. Methods Appl. Mech. Eng. 351, 184-225 (2019). MSC: 74A45 35Q74 74S20 65M06 65M12 65M15 74H55 PDFBibTeX XMLCite \textit{P. K. Jha} and \textit{R. Lipton}, Comput. Methods Appl. Mech. Eng. 351, 184--225 (2019; Zbl 1441.74018) Full Text: DOI arXiv
Nikpayam, Jaber; Kouchakzadeh, Mohammad Ali A variable horizon method for coupling meshfree peridynamics to FEM. (English) Zbl 1441.74024 Comput. Methods Appl. Mech. Eng. 355, 308-322 (2019). MSC: 74A45 74S05 65M60 PDFBibTeX XMLCite \textit{J. Nikpayam} and \textit{M. A. Kouchakzadeh}, Comput. Methods Appl. Mech. Eng. 355, 308--322 (2019; Zbl 1441.74024) Full Text: DOI
Madenci, Erdogan; Dorduncu, Mehmet; Gu, Xin Peridynamic least squares minimization. (English) Zbl 1440.74477 Comput. Methods Appl. Mech. Eng. 348, 846-874 (2019). MSC: 74S99 65D99 74A99 PDFBibTeX XMLCite \textit{E. Madenci} et al., Comput. Methods Appl. Mech. Eng. 348, 846--874 (2019; Zbl 1440.74477) Full Text: DOI
Wang, Xiaonan; Kulkarni, Shank S.; Tabarraei, Alireza Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems. (English) Zbl 1440.74041 Comput. Methods Appl. Mech. Eng. 344, 251-275 (2019). MSC: 74A45 74S05 65M60 PDFBibTeX XMLCite \textit{X. Wang} et al., Comput. Methods Appl. Mech. Eng. 344, 251--275 (2019; Zbl 1440.74041) Full Text: DOI
Trask, Nathaniel; You, Huaiqian; Yu, Yue; Parks, Michael L. An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics. (English) Zbl 1440.74463 Comput. Methods Appl. Mech. Eng. 343, 151-165 (2019). MSC: 74S20 65M06 65D30 74A45 PDFBibTeX XMLCite \textit{N. Trask} et al., Comput. Methods Appl. Mech. Eng. 343, 151--165 (2019; Zbl 1440.74463) Full Text: DOI arXiv
Shojaei, Arman; Galvanetto, Ugo; Rabczuk, Timon; Jenabi, Ali; Zaccariotto, Mirco A generalized finite difference method based on the peridynamic differential operator for the solution of problems in bounded and unbounded domains. (English) Zbl 1440.65157 Comput. Methods Appl. Mech. Eng. 343, 100-126 (2019). MSC: 65N06 PDFBibTeX XMLCite \textit{A. Shojaei} et al., Comput. Methods Appl. Mech. Eng. 343, 100--126 (2019; Zbl 1440.65157) Full Text: DOI
Zhao, Wei; Hon, Y. C. An accurate and efficient numerical method for solving linear peridynamic models. (English) Zbl 1481.65200 Appl. Math. Modelling 74, 113-131 (2019). MSC: 65M70 74A45 PDFBibTeX XMLCite \textit{W. Zhao} and \textit{Y. C. Hon}, Appl. Math. Modelling 74, 113--131 (2019; Zbl 1481.65200) Full Text: DOI
Fu, Shubin; Gao, Kai; Gibson, Richard L. jun.; Chung, Eric T. An efficient high-order multiscale finite element method for frequency-domain elastic wave modeling. (English) Zbl 1425.74234 Comput. Geosci. 23, No. 5, 997-1010 (2019). MSC: 74J05 65N30 86A17 PDFBibTeX XMLCite \textit{S. Fu} et al., Comput. Geosci. 23, No. 5, 997--1010 (2019; Zbl 1425.74234) Full Text: DOI Link
Du, Qiang; Yin, Xiaobo A conforming DG method for linear nonlocal models with integrable kernels. (English) Zbl 1428.82037 J. Sci. Comput. 80, No. 3, 1913-1935 (2019). MSC: 82C21 65R20 74S05 46N20 45A05 65N30 PDFBibTeX XMLCite \textit{Q. Du} and \textit{X. Yin}, J. Sci. Comput. 80, No. 3, 1913--1935 (2019; Zbl 1428.82037) Full Text: DOI arXiv
Du, Qiang; Ju, Lili; Lu, Jianfang A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems. (English) Zbl 1405.65118 Math. Comput. 88, No. 315, 123-147 (2019). Reviewer: Elena V. Tabarintseva (Chelyabinsk) MSC: 65M60 45K05 35R09 PDFBibTeX XMLCite \textit{Q. Du} et al., Math. Comput. 88, No. 315, 123--147 (2019; Zbl 1405.65118) Full Text: DOI
Du, Qiang; Zhang, Jiwei; Zheng, Chunxiong Nonlocal wave propagation in unbounded multi-scale media. (English) Zbl 1475.65156 Commun. Comput. Phys. 24, No. 4, 1049-1072 (2018). MSC: 65M99 35R09 45K05 82C21 65R20 PDFBibTeX XMLCite \textit{Q. Du} et al., Commun. Comput. Phys. 24, No. 4, 1049--1072 (2018; Zbl 1475.65156) Full Text: DOI
Pasetto, Marco; Leng, Yu; Chen, Jiun-Shyan; Foster, John T.; Seleson, Pablo A reproducing kernel enhanced approach for peridynamic solutions. (English) Zbl 1440.74478 Comput. Methods Appl. Mech. Eng. 340, 1044-1078 (2018). MSC: 74S99 65M99 74A45 PDFBibTeX XMLCite \textit{M. Pasetto} et al., Comput. Methods Appl. Mech. Eng. 340, 1044--1078 (2018; Zbl 1440.74478) Full Text: DOI Link
Nguyen, Vinh Phu; Wu, Jian-Ying Modeling dynamic fracture of solids with a phase-field regularized cohesive zone model. (English) Zbl 1440.74362 Comput. Methods Appl. Mech. Eng. 340, 1000-1022 (2018). MSC: 74R10 74S05 65M60 PDFBibTeX XMLCite \textit{V. P. Nguyen} and \textit{J.-Y. Wu}, Comput. Methods Appl. Mech. Eng. 340, 1000--1022 (2018; Zbl 1440.74362) Full Text: DOI
Yu, Yue; Bargos, Fabiano F.; You, Huaiqian; Parks, Michael L.; Bittencourt, Marco L.; Karniadakis, George E. A partitioned coupling framework for peridynamics and classical theory: analysis and simulations. (English) Zbl 1440.74045 Comput. Methods Appl. Mech. Eng. 340, 905-931 (2018). MSC: 74A45 74S05 65N30 PDFBibTeX XMLCite \textit{Y. Yu} et al., Comput. Methods Appl. Mech. Eng. 340, 905--931 (2018; Zbl 1440.74045) Full Text: DOI
Nicely, Clint; Tang, Shaoqiang; Qian, Dong Nonlocal matching boundary conditions for non-ordinary peridynamics with correspondence material model. (English) Zbl 1440.74033 Comput. Methods Appl. Mech. Eng. 338, 463-490 (2018). MSC: 74A45 74S05 65M60 PDFBibTeX XMLCite \textit{C. Nicely} et al., Comput. Methods Appl. Mech. Eng. 338, 463--490 (2018; Zbl 1440.74033) Full Text: DOI
Bie, Y. H.; Cui, X. Y.; Li, Z. C. A coupling approach of state-based peridynamics with node-based smoothed finite element method. (English) Zbl 1439.74392 Comput. Methods Appl. Mech. Eng. 331, 675-700 (2018). MSC: 74S05 65M60 74A45 PDFBibTeX XMLCite \textit{Y. H. Bie} et al., Comput. Methods Appl. Mech. Eng. 331, 675--700 (2018; Zbl 1439.74392) Full Text: DOI
Zaccariotto, Mirco; Mudric, Teo; Tomasi, Davide; Shojaei, Arman; Galvanetto, Ugo Coupling of FEM meshes with peridynamic grids. (English) Zbl 1439.65103 Comput. Methods Appl. Mech. Eng. 330, 471-497 (2018). MSC: 65M50 65M60 PDFBibTeX XMLCite \textit{M. Zaccariotto} et al., Comput. Methods Appl. Mech. Eng. 330, 471--497 (2018; Zbl 1439.65103) Full Text: DOI
Xue, Tao; Zhang, Xiaobing; Tamma, Kumar K. A two-field state-based peridynamic theory for thermal contact problems. (English) Zbl 1416.65588 J. Comput. Phys. 374, 1180-1195 (2018). MSC: 65Z05 65L80 80A17 PDFBibTeX XMLCite \textit{T. Xue} et al., J. Comput. Phys. 374, 1180--1195 (2018; Zbl 1416.65588) Full Text: DOI
Antonietti, Paola F.; Ferroni, Alberto; Mazzieri, Ilario; Paolucci, Roberto; Quarteroni, Alfio; Smerzini, Chiara; Stupazzini, Marco Numerical modeling of seismic waves by discontinuous spectral element methods. (English) Zbl 1453.86013 ESAIM, Proc. Surv. 61, 1-37 (2018). MSC: 86-10 86-08 65M70 86A15 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., ESAIM, Proc. Surv. 61, 1--37 (2018; Zbl 1453.86013) Full Text: DOI
Liu, Huan; Cheng, Aijie; Wang, Hong A fast discontinuous Galerkin method for a bond-based linear peridynamic model discretized on a locally refined composite mesh. (English) Zbl 1397.65279 J. Sci. Comput. 76, No. 2, 913-942 (2018). MSC: 65N30 65N50 65F08 65F10 15B05 65N12 PDFBibTeX XMLCite \textit{H. Liu} et al., J. Sci. Comput. 76, No. 2, 913--942 (2018; Zbl 1397.65279) Full Text: DOI
Zhang, Xiaoping; Wu, Jiming; Ju, Lili An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems. (English) Zbl 1405.65158 Appl. Numer. Math. 133, 52-68 (2018). Reviewer: Andreas Kleefeld (Jülich) MSC: 65N35 74S25 65D32 15B05 65R20 PDFBibTeX XMLCite \textit{X. Zhang} et al., Appl. Numer. Math. 133, 52--68 (2018; Zbl 1405.65158) Full Text: DOI
Liu, Zhengguang; Li, Xiaoli A fast finite difference method for a continuous static linear bond-based peridynamics model of mechanics. (English) Zbl 1398.65216 J. Sci. Comput. 74, No. 2, 728-742 (2018). MSC: 65M06 65M12 65M15 74S20 65T50 PDFBibTeX XMLCite \textit{Z. Liu} and \textit{X. Li}, J. Sci. Comput. 74, No. 2, 728--742 (2018; Zbl 1398.65216) Full Text: DOI
Tian, Hao; Ju, Lili; Du, Qiang A conservative nonlocal convection-diffusion model and asymptotically compatible finite difference discretization. (English) Zbl 1439.65134 Comput. Methods Appl. Mech. Eng. 320, 46-67 (2017). MSC: 65N06 65N12 PDFBibTeX XMLCite \textit{H. Tian} et al., Comput. Methods Appl. Mech. Eng. 320, 46--67 (2017; Zbl 1439.65134) Full Text: DOI
Rabinovich, Daniel; Givoli, Dan; Bielak, Jacobo; Hagstrom, Thomas The double absorbing boundary method for a class of anisotropic elastic media. (English) Zbl 1439.74085 Comput. Methods Appl. Mech. Eng. 315, 190-221 (2017). MSC: 74E10 74S05 65M60 PDFBibTeX XMLCite \textit{D. Rabinovich} et al., Comput. Methods Appl. Mech. Eng. 315, 190--221 (2017; Zbl 1439.74085) Full Text: DOI
Tao, Yunzhe; Tian, Xiaochuan; Du, Qiang Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. (English) Zbl 1411.74058 Appl. Math. Comput. 305, 282-298 (2017). MSC: 74S05 65N30 45K05 74A45 PDFBibTeX XMLCite \textit{Y. Tao} et al., Appl. Math. Comput. 305, 282--298 (2017; Zbl 1411.74058) Full Text: DOI
Diehl, Patrick; Bußler, Michael; Pflüger, Dirk; Frey, Steffen; Ertl, Thomas; Sadlo, Filip; Schweitzer, Marc Alexander Extraction of fragments and waves after impact damage in particle-based simulations. (English) Zbl 1446.74184 Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations VIII. Selected contributions based on the presentations at the 8th international workshop, Bonn, Germany, September 7–9, 2015. Cham: Springer. Lect. Notes Comput. Sci. Eng. 115, 17-34 (2017). MSC: 74M20 74R05 74A70 65R20 74-10 74A45 74-04 74-05 PDFBibTeX XMLCite \textit{P. Diehl} et al., Lect. Notes Comput. Sci. Eng. 115, 17--34 (2017; Zbl 1446.74184) Full Text: DOI
Mossaiby, F.; Shojaei, A.; Zaccariotto, M.; Galvanetto, U. OpenCL implementation of a high performance 3D peridynamic model on graphics accelerators. (English) Zbl 1524.74004 Comput. Math. Appl. 74, No. 8, 1856-1870 (2017). MSC: 74-04 65Y05 65Y10 74R10 74S05 PDFBibTeX XMLCite \textit{F. Mossaiby} et al., Comput. Math. Appl. 74, No. 8, 1856--1870 (2017; Zbl 1524.74004) Full Text: DOI
Giraldo, Daniel; Restrepo, Doriam The spectral cell method in nonlinear earthquake modeling. (English) Zbl 1398.74331 Comput. Mech. 60, No. 6, 883-903 (2017). MSC: 74S05 86A15 74S30 65N30 74S25 PDFBibTeX XMLCite \textit{D. Giraldo} and \textit{D. Restrepo}, Comput. Mech. 60, No. 6, 883--903 (2017; Zbl 1398.74331) Full Text: DOI Link
Wang, Che; Wang, Hong A fast collocation method for a variable-coefficient nonlocal diffusion model. (English) Zbl 1380.65448 J. Comput. Phys. 330, 114-126 (2017). MSC: 65R20 35R11 PDFBibTeX XMLCite \textit{C. Wang} and \textit{H. Wang}, J. Comput. Phys. 330, 114--126 (2017; Zbl 1380.65448) Full Text: DOI
Du, Qiang; Yang, Jiang Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications. (English) Zbl 1380.65435 J. Comput. Phys. 332, 118-134 (2017). MSC: 65R20 45J05 PDFBibTeX XMLCite \textit{Q. Du} and \textit{J. Yang}, J. Comput. Phys. 332, 118--134 (2017; Zbl 1380.65435) Full Text: DOI
Liu, Zhengguang; Cheng, Aijie; Wang, Hong An \(hp\)-Galerkin method with fast solution for linear peridynamic models in one dimension. (English) Zbl 1372.65310 Comput. Math. Appl. 73, No. 7, 1546-1565 (2017). MSC: 65N30 65T50 65N50 35J25 15B05 PDFBibTeX XMLCite \textit{Z. Liu} et al., Comput. Math. Appl. 73, No. 7, 1546--1565 (2017; Zbl 1372.65310) Full Text: DOI
Zou, Zilong; Aquino, Wilkins; Harari, Isaac Nitsche’s method for Helmholtz problems with embedded interfaces. (English) Zbl 1365.35018 Int. J. Numer. Methods Eng. 110, No. 7, 618-636 (2017). MSC: 35J05 35A25 35B40 35B30 65L60 65M60 PDFBibTeX XMLCite \textit{Z. Zou} et al., Int. J. Numer. Methods Eng. 110, No. 7, 618--636 (2017; Zbl 1365.35018) Full Text: DOI Link
Seleson, Pablo; Littlewood, David J. Convergence studies in meshfree peridynamic simulations. (English) Zbl 1443.65253 Comput. Math. Appl. 71, No. 11, 2432-2448 (2016). MSC: 65M70 74A45 PDFBibTeX XMLCite \textit{P. Seleson} and \textit{D. J. Littlewood}, Comput. Math. Appl. 71, No. 11, 2432--2448 (2016; Zbl 1443.65253) Full Text: DOI
Seleson, Pablo; Du, Qiang; Parks, Michael L. On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models. (English) Zbl 1439.74044 Comput. Methods Appl. Mech. Eng. 311, 698-722 (2016). MSC: 74B05 45K05 65R20 70C20 74S20 PDFBibTeX XMLCite \textit{P. Seleson} et al., Comput. Methods Appl. Mech. Eng. 311, 698--722 (2016; Zbl 1439.74044) Full Text: DOI
Zhang, Xuhao; Wang, Hong A fast collocation method for a static bond-based linear peridynamic model. (English) Zbl 1439.74493 Comput. Methods Appl. Mech. Eng. 311, 280-303 (2016). MSC: 74S25 65N35 74A45 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{H. Wang}, Comput. Methods Appl. Mech. Eng. 311, 280--303 (2016; Zbl 1439.74493) Full Text: DOI